SOLUTION: Solve logx + log(x-48) = 2

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Question 105757: Solve logx + log(x-48) = 2
Found 2 solutions by HyperBrain, MathTherapy:
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
log%28x%29+%2B+log%28x-48%29+=+2
Read my lesson,"An overview to the laws of logarithms"

log%28x%28x-48%29%29=2
The antilogarithm of any number a, is the number who has a logarithm of a.

antilog%28log%28x%28x-48%29%29%29=antilog%282%29

Take note that log%2810%5E2%29=2. Thus, antilog%282%29=10%5E2=100
x%28x-48%29=100
x%5E2-48x=100
x%5E2-48x-100=0
By the quadratic formula,
x=%2848%2B-sqrt%2848%5E2-4%2A1%2A%28-100%29%29%29%2F%282%2A1%29
x=%2848%2B-sqrt%282304%2B400%29%29%2F%282%29
x=%2848%2B-sqrt%282704%29%29%2F%282%29
x=%2848%2B-+52%29%2F%282%29
x=-2 or x=50

Power up,
HyperBrain!

Answer by MathTherapy(10858) About Me  (Show Source):
You can put this solution on YOUR website!
Solve logx + log(x-48) = 2
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As usual, HyperBrain(694)'s solution is PARTIALLY-CORRECT/WRONG.
Furthermore, the TRINOMIAL, x%5E2+-+48x+-+100 can be factorized into (x - 50)(x + 2), so, using the QUADRATIC EQUATION formula is UNNECESSARY,
as it NOTICEABLY generates LARGE numbers, which most of us deplore!! Unless, of course, one wishes to do so! 

log (x) + log (x - 48) = 2
Finally, as the SMALLER of the 2 log variable-arguments, x - 48 MUST be > 0, we get: x - 48 > 0_____x > 48.
So, equation becomes: log (x) + log (x - 48) = 2, with x > 48.

One of the respondent's 2 solutions, - 2 is NOT > 48, which makes it, EXTRANEOUS. Obviously, the other solution, x = 50 is EFINITELY > 48, making
it VALID/ACCEPTABLE, and therefore, the SOLE SOLUTION.